A uniform rope of length L and mass $$m1$$ hangs vertically from a rigid support. A block of mass $$m2is$$ attached to the free end of the rope. A transverse pulse of wavelength λ$$1$$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is λ$$2$$. The ratio λ$$2$$λ$$1$$ is

Question

A uniform rope of length L and mass $$m1$$ hangs vertically from a rigid support. A block of mass $$m2is$$ attached to the free end of the rope. A transverse pulse of wavelength λ$$1$$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is λ$$2$$. The ratio λ$$2$$λ$$1$$ is

Infinity Learn · Accepted Answer

Wavelength of pulse at the lower  end λ$$1$$∝ velocity $$v1=T1$$μ Similarly, λ$$2$$∝$$v2=T2$$μ∴λ$$2$$λ$$1=T2T1=m1+m2gm2g=m1+m2m2$$

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